Apple Store prompting for passwords to two sets of apple ids

I broke my iPhone 6 and went back to using my old iPhone 4 as a spare, which my dad used briefly. Now, when I logged into the phone with my apple id, the App Store is prompting for my father's id in some cases and mine, in others. I've already logged him out and logged in with my id. Despite resetting all data and restarting the phone, though, I'm unable to download any apps, through either ids. Any idea how I can fix this?